TSTP Solution File: ITP015+2 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : ITP015+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat May  4 08:08:55 EDT 2024

% Result   : Theorem 3.54s 0.88s
% Output   : CNFRefutation 3.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   72 (  24 unt;   0 def)
%            Number of atoms       :  227 (  47 equ)
%            Maximal formula atoms :   37 (   3 avg)
%            Number of connectives :  263 ( 108   ~; 105   |;  18   &)
%                                         (   9 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    6 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  12 con; 0-2 aty)
%            Number of variables   :   85 (   0 sgn  44   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ax_false_p,axiom,
    ~ p(c_2Ebool_2EF),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',ax_false_p) ).

fof(ap_tp,axiom,
    ! [X1,X2,X3] :
      ( mem(X3,arr(X1,X2))
     => ! [X4] :
          ( mem(X4,X1)
         => mem(ap(X3,X4),X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',ap_tp) ).

fof(boolext,axiom,
    ! [X5] :
      ( mem(X5,bool)
     => ! [X6] :
          ( mem(X6,bool)
         => ( ( p(X5)
            <=> p(X6) )
           => X5 = X6 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',boolext) ).

fof(mem_c_2Einteger_2Eint__lt,axiom,
    mem(c_2Einteger_2Eint__lt,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool))),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',mem_c_2Einteger_2Eint__lt) ).

fof(mem_c_2Ebool_2EF,axiom,
    mem(c_2Ebool_2EF,bool),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',mem_c_2Ebool_2EF) ).

fof(mem_c_2Einteger_2Eint__of__num,axiom,
    mem(c_2Einteger_2Eint__of__num,arr(ty_2Enum_2Enum,ty_2Einteger_2Eint)),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',mem_c_2Einteger_2Eint__of__num) ).

fof(mem_c_2Einteger_2Eint__neg,axiom,
    mem(c_2Einteger_2Eint__neg,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',mem_c_2Einteger_2Eint__neg) ).

fof(conj_thm_2Einteger_2EINT__LT__CALCULATE,axiom,
    ! [X26] :
      ( mem(X26,ty_2Enum_2Enum)
     => ! [X27] :
          ( mem(X27,ty_2Enum_2Enum)
         => ( ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,X26)),ap(c_2Einteger_2Eint__of__num,X27)))
            <=> p(ap(ap(c_2Eprim__rec_2E_3C,X26),X27)) )
            & ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X26))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X27))))
            <=> p(ap(ap(c_2Eprim__rec_2E_3C,X27),X26)) )
            & ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X26))),ap(c_2Einteger_2Eint__of__num,X27)))
            <=> ( X26 != c_2Enum_2E0
                | X27 != c_2Enum_2E0 ) )
            & ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,X26)),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X27))))
            <=> ~ $true ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',conj_thm_2Einteger_2EINT__LT__CALCULATE) ).

fof(mem_c_2Enum_2E0,axiom,
    mem(c_2Enum_2E0,ty_2Enum_2Enum),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',mem_c_2Enum_2E0) ).

fof(ax_thm_2Einteger__word_2Ei2w__def,axiom,
    ! [X9] :
      ( ne(X9)
     => ! [X28] :
          ( mem(X28,ty_2Einteger_2Eint)
         => ap(c_2Einteger__word_2Ei2w(X9),X28) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X9)),ap(ap(c_2Einteger_2Eint__lt,X28),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),ap(c_2Ewords_2Eword__2comp(X9),ap(c_2Ewords_2En2w(X9),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,X28))))),ap(c_2Ewords_2En2w(X9),ap(c_2Einteger_2ENum,X28))) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',ax_thm_2Einteger__word_2Ei2w__def) ).

fof(conj_thm_2Einteger_2ENUM__OF__INT,axiom,
    ! [X26] :
      ( mem(X26,ty_2Enum_2Enum)
     => ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,X26)) = X26 ),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',conj_thm_2Einteger_2ENUM__OF__INT) ).

fof(conj_thm_2Einteger_2EINT__NEG__0,axiom,
    ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',conj_thm_2Einteger_2EINT__NEG__0) ).

fof(conj_thm_2Ewords_2EWORD__NEG__0,axiom,
    ! [X9] :
      ( ne(X9)
     => ap(c_2Ewords_2Eword__2comp(X9),ap(c_2Ewords_2En2w(X9),c_2Enum_2E0)) = ap(c_2Ewords_2En2w(X9),c_2Enum_2E0) ),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',conj_thm_2Ewords_2EWORD__NEG__0) ).

fof(conj_thm_2Ebool_2Ebool__case__thm,axiom,
    ! [X9] :
      ( ne(X9)
     => ( ! [X12] :
            ( mem(X12,X9)
           => ! [X13] :
                ( mem(X13,X9)
               => ap(ap(ap(c_2Ebool_2ECOND(X9),c_2Ebool_2ET),X12),X13) = X12 ) )
        & ! [X24] :
            ( mem(X24,X9)
           => ! [X25] :
                ( mem(X25,X9)
               => ap(ap(ap(c_2Ebool_2ECOND(X9),c_2Ebool_2EF),X24),X25) = X25 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',conj_thm_2Ebool_2Ebool__case__thm) ).

fof(mem_c_2Ewords_2En2w,axiom,
    ! [X9] :
      ( ne(X9)
     => mem(c_2Ewords_2En2w(X9),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,X9))) ),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',mem_c_2Ewords_2En2w) ).

fof(conj_thm_2Einteger__word_2Ei2w__0,conjecture,
    ! [X9] :
      ( ne(X9)
     => ap(c_2Einteger__word_2Ei2w(X9),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = ap(c_2Ewords_2En2w(X9),c_2Enum_2E0) ),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',conj_thm_2Einteger__word_2Ei2w__0) ).

fof(ne_ty_2Efcp_2Ecart,axiom,
    ! [X10] :
      ( ne(X10)
     => ! [X11] :
          ( ne(X11)
         => ne(ty_2Efcp_2Ecart(X10,X11)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',ne_ty_2Efcp_2Ecart) ).

fof(bool_ne,axiom,
    ne(bool),
    file('/export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p',bool_ne) ).

fof(c_0_18,plain,
    ~ p(c_2Ebool_2EF),
    inference(fof_simplification,[status(thm)],[ax_false_p]) ).

fof(c_0_19,plain,
    ! [X32,X33,X34,X35] :
      ( ~ mem(X34,arr(X32,X33))
      | ~ mem(X35,X32)
      | mem(ap(X34,X35),X33) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).

fof(c_0_20,plain,
    ! [X69,X70] :
      ( ( ~ p(X69)
        | ~ p(X70)
        | X69 = X70
        | ~ mem(X70,bool)
        | ~ mem(X69,bool) )
      & ( p(X69)
        | p(X70)
        | X69 = X70
        | ~ mem(X70,bool)
        | ~ mem(X69,bool) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[boolext])])])])]) ).

fof(c_0_21,plain,
    ~ p(c_2Ebool_2EF),
    inference(fof_nnf,[status(thm)],[c_0_18]) ).

cnf(c_0_22,plain,
    ( mem(ap(X1,X4),X3)
    | ~ mem(X1,arr(X2,X3))
    | ~ mem(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,plain,
    mem(c_2Einteger_2Eint__lt,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool))),
    inference(split_conjunct,[status(thm)],[mem_c_2Einteger_2Eint__lt]) ).

cnf(c_0_24,plain,
    ( p(X1)
    | p(X2)
    | X1 = X2
    | ~ mem(X2,bool)
    | ~ mem(X1,bool) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,plain,
    mem(c_2Ebool_2EF,bool),
    inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF]) ).

cnf(c_0_26,plain,
    ~ p(c_2Ebool_2EF),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,plain,
    ( mem(ap(c_2Einteger_2Eint__lt,X1),arr(ty_2Einteger_2Eint,bool))
    | ~ mem(X1,ty_2Einteger_2Eint) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_28,plain,
    ( X1 = c_2Ebool_2EF
    | p(X1)
    | ~ mem(X1,bool) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_29,plain,
    ( mem(ap(ap(c_2Einteger_2Eint__lt,X1),X2),bool)
    | ~ mem(X2,ty_2Einteger_2Eint)
    | ~ mem(X1,ty_2Einteger_2Eint) ),
    inference(spm,[status(thm)],[c_0_22,c_0_27]) ).

cnf(c_0_30,plain,
    mem(c_2Einteger_2Eint__of__num,arr(ty_2Enum_2Enum,ty_2Einteger_2Eint)),
    inference(split_conjunct,[status(thm)],[mem_c_2Einteger_2Eint__of__num]) ).

cnf(c_0_31,plain,
    ( ap(ap(c_2Einteger_2Eint__lt,X1),X2) = c_2Ebool_2EF
    | p(ap(ap(c_2Einteger_2Eint__lt,X1),X2))
    | ~ mem(X2,ty_2Einteger_2Eint)
    | ~ mem(X1,ty_2Einteger_2Eint) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_32,plain,
    ( mem(ap(c_2Einteger_2Eint__of__num,X1),ty_2Einteger_2Eint)
    | ~ mem(X1,ty_2Enum_2Enum) ),
    inference(spm,[status(thm)],[c_0_22,c_0_30]) ).

cnf(c_0_33,plain,
    mem(c_2Einteger_2Eint__neg,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)),
    inference(split_conjunct,[status(thm)],[mem_c_2Einteger_2Eint__neg]) ).

cnf(c_0_34,plain,
    ( ap(ap(c_2Einteger_2Eint__lt,X1),ap(c_2Einteger_2Eint__of__num,X2)) = c_2Ebool_2EF
    | p(ap(ap(c_2Einteger_2Eint__lt,X1),ap(c_2Einteger_2Eint__of__num,X2)))
    | ~ mem(X1,ty_2Einteger_2Eint)
    | ~ mem(X2,ty_2Enum_2Enum) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_35,plain,
    ( mem(ap(c_2Einteger_2Eint__neg,X1),ty_2Einteger_2Eint)
    | ~ mem(X1,ty_2Einteger_2Eint) ),
    inference(spm,[status(thm)],[c_0_22,c_0_33]) ).

fof(c_0_36,plain,
    ! [X26] :
      ( mem(X26,ty_2Enum_2Enum)
     => ! [X27] :
          ( mem(X27,ty_2Enum_2Enum)
         => ( ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,X26)),ap(c_2Einteger_2Eint__of__num,X27)))
            <=> p(ap(ap(c_2Eprim__rec_2E_3C,X26),X27)) )
            & ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X26))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X27))))
            <=> p(ap(ap(c_2Eprim__rec_2E_3C,X27),X26)) )
            & ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X26))),ap(c_2Einteger_2Eint__of__num,X27)))
            <=> ( X26 != c_2Enum_2E0
                | X27 != c_2Enum_2E0 ) )
            & ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,X26)),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X27))))
            <=> ~ $true ) ) ) ),
    inference(fof_simplification,[status(thm)],[conj_thm_2Einteger_2EINT__LT__CALCULATE]) ).

cnf(c_0_37,plain,
    ( ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,X1)),ap(c_2Einteger_2Eint__of__num,X2)) = c_2Ebool_2EF
    | p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,X1)),ap(c_2Einteger_2Eint__of__num,X2)))
    | ~ mem(X2,ty_2Enum_2Enum)
    | ~ mem(X1,ty_2Einteger_2Eint) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,plain,
    mem(c_2Enum_2E0,ty_2Enum_2Enum),
    inference(split_conjunct,[status(thm)],[mem_c_2Enum_2E0]) ).

fof(c_0_39,plain,
    ! [X48,X49] :
      ( ( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,X48)),ap(c_2Einteger_2Eint__of__num,X49)))
        | p(ap(ap(c_2Eprim__rec_2E_3C,X48),X49))
        | ~ mem(X49,ty_2Enum_2Enum)
        | ~ mem(X48,ty_2Enum_2Enum) )
      & ( ~ p(ap(ap(c_2Eprim__rec_2E_3C,X48),X49))
        | p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,X48)),ap(c_2Einteger_2Eint__of__num,X49)))
        | ~ mem(X49,ty_2Enum_2Enum)
        | ~ mem(X48,ty_2Enum_2Enum) )
      & ( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X48))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X49))))
        | p(ap(ap(c_2Eprim__rec_2E_3C,X49),X48))
        | ~ mem(X49,ty_2Enum_2Enum)
        | ~ mem(X48,ty_2Enum_2Enum) )
      & ( ~ p(ap(ap(c_2Eprim__rec_2E_3C,X49),X48))
        | p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X48))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X49))))
        | ~ mem(X49,ty_2Enum_2Enum)
        | ~ mem(X48,ty_2Enum_2Enum) )
      & ( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X48))),ap(c_2Einteger_2Eint__of__num,X49)))
        | X48 != c_2Enum_2E0
        | X49 != c_2Enum_2E0
        | ~ mem(X49,ty_2Enum_2Enum)
        | ~ mem(X48,ty_2Enum_2Enum) )
      & ( X48 = c_2Enum_2E0
        | p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X48))),ap(c_2Einteger_2Eint__of__num,X49)))
        | ~ mem(X49,ty_2Enum_2Enum)
        | ~ mem(X48,ty_2Enum_2Enum) )
      & ( X49 = c_2Enum_2E0
        | p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X48))),ap(c_2Einteger_2Eint__of__num,X49)))
        | ~ mem(X49,ty_2Enum_2Enum)
        | ~ mem(X48,ty_2Enum_2Enum) )
      & ( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,X48)),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X49))))
        | ~ $true
        | ~ mem(X49,ty_2Enum_2Enum)
        | ~ mem(X48,ty_2Enum_2Enum) )
      & ( $true
        | p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,X48)),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X49))))
        | ~ mem(X49,ty_2Enum_2Enum)
        | ~ mem(X48,ty_2Enum_2Enum) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])])]) ).

fof(c_0_40,plain,
    ! [X50,X51] :
      ( ~ ne(X50)
      | ~ mem(X51,ty_2Einteger_2Eint)
      | ap(c_2Einteger__word_2Ei2w(X50),X51) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X50)),ap(ap(c_2Einteger_2Eint__lt,X51),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),ap(c_2Ewords_2Eword__2comp(X50),ap(c_2Ewords_2En2w(X50),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,X51))))),ap(c_2Ewords_2En2w(X50),ap(c_2Einteger_2ENum,X51))) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Einteger__word_2Ei2w__def])])])]) ).

fof(c_0_41,plain,
    ! [X58] :
      ( ~ mem(X58,ty_2Enum_2Enum)
      | ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,X58)) = X58 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Einteger_2ENUM__OF__INT])])]) ).

cnf(c_0_42,plain,
    ( ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,X1)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = c_2Ebool_2EF
    | p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,X1)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)))
    | ~ mem(X1,ty_2Einteger_2Eint) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_43,plain,
    ( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X1))),ap(c_2Einteger_2Eint__of__num,X2)))
    | X1 != c_2Enum_2E0
    | X2 != c_2Enum_2E0
    | ~ mem(X2,ty_2Enum_2Enum)
    | ~ mem(X1,ty_2Enum_2Enum) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_44,plain,
    ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),
    inference(split_conjunct,[status(thm)],[conj_thm_2Einteger_2EINT__NEG__0]) ).

cnf(c_0_45,plain,
    ( ap(c_2Einteger__word_2Ei2w(X1),X2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X1)),ap(ap(c_2Einteger_2Eint__lt,X2),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),ap(c_2Ewords_2Eword__2comp(X1),ap(c_2Ewords_2En2w(X1),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,X2))))),ap(c_2Ewords_2En2w(X1),ap(c_2Einteger_2ENum,X2)))
    | ~ ne(X1)
    | ~ mem(X2,ty_2Einteger_2Eint) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_46,plain,
    ( ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,X1)) = X1
    | ~ mem(X1,ty_2Enum_2Enum) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_47,plain,
    ( ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X1))),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = c_2Ebool_2EF
    | p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X1))),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)))
    | ~ mem(X1,ty_2Enum_2Enum) ),
    inference(spm,[status(thm)],[c_0_42,c_0_32]) ).

cnf(c_0_48,plain,
    ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_43])]),c_0_44]),c_0_38])]) ).

cnf(c_0_49,plain,
    ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X1)),ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,X2)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),ap(c_2Ewords_2Eword__2comp(X1),ap(c_2Ewords_2En2w(X1),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,X2)))))),ap(c_2Ewords_2En2w(X1),X2)) = ap(c_2Einteger__word_2Ei2w(X1),ap(c_2Einteger_2Eint__of__num,X2))
    | ~ mem(X2,ty_2Enum_2Enum)
    | ~ ne(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_32]) ).

cnf(c_0_50,plain,
    ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = c_2Ebool_2EF,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_38]),c_0_44]),c_0_44]),c_0_48]) ).

cnf(c_0_51,plain,
    ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X1)),c_2Ebool_2EF),ap(c_2Ewords_2Eword__2comp(X1),ap(c_2Ewords_2En2w(X1),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))))),ap(c_2Ewords_2En2w(X1),c_2Enum_2E0)) = ap(c_2Einteger__word_2Ei2w(X1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))
    | ~ ne(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_50]),c_0_38])]) ).

fof(c_0_52,plain,
    ! [X53] :
      ( ~ ne(X53)
      | ap(c_2Ewords_2Eword__2comp(X53),ap(c_2Ewords_2En2w(X53),c_2Enum_2E0)) = ap(c_2Ewords_2En2w(X53),c_2Enum_2E0) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ewords_2EWORD__NEG__0])])]) ).

fof(c_0_53,plain,
    ! [X78,X79,X80,X81,X82] :
      ( ( ~ mem(X79,X78)
        | ~ mem(X80,X78)
        | ap(ap(ap(c_2Ebool_2ECOND(X78),c_2Ebool_2ET),X79),X80) = X79
        | ~ ne(X78) )
      & ( ~ mem(X81,X78)
        | ~ mem(X82,X78)
        | ap(ap(ap(c_2Ebool_2ECOND(X78),c_2Ebool_2EF),X81),X82) = X82
        | ~ ne(X78) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ebool_2Ebool__case__thm])])])])]) ).

cnf(c_0_54,plain,
    ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X1)),c_2Ebool_2EF),ap(c_2Ewords_2Eword__2comp(X1),ap(c_2Ewords_2En2w(X1),c_2Enum_2E0))),ap(c_2Ewords_2En2w(X1),c_2Enum_2E0)) = ap(c_2Einteger__word_2Ei2w(X1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))
    | ~ ne(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_46]),c_0_38])]) ).

cnf(c_0_55,plain,
    ( ap(c_2Ewords_2Eword__2comp(X1),ap(c_2Ewords_2En2w(X1),c_2Enum_2E0)) = ap(c_2Ewords_2En2w(X1),c_2Enum_2E0)
    | ~ ne(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

fof(c_0_56,plain,
    ! [X54] :
      ( ~ ne(X54)
      | mem(c_2Ewords_2En2w(X54),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,X54))) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Ewords_2En2w])])]) ).

fof(c_0_57,negated_conjecture,
    ~ ! [X9] :
        ( ne(X9)
       => ap(c_2Einteger__word_2Ei2w(X9),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = ap(c_2Ewords_2En2w(X9),c_2Enum_2E0) ),
    inference(assume_negation,[status(cth)],[conj_thm_2Einteger__word_2Ei2w__0]) ).

cnf(c_0_58,plain,
    ( ap(ap(ap(c_2Ebool_2ECOND(X2),c_2Ebool_2EF),X1),X3) = X3
    | ~ mem(X1,X2)
    | ~ mem(X3,X2)
    | ~ ne(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_59,plain,
    ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X1)),c_2Ebool_2EF),ap(c_2Ewords_2En2w(X1),c_2Enum_2E0)),ap(c_2Ewords_2En2w(X1),c_2Enum_2E0)) = ap(c_2Einteger__word_2Ei2w(X1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))
    | ~ ne(X1) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_60,plain,
    ( mem(c_2Ewords_2En2w(X1),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,X1)))
    | ~ ne(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

fof(c_0_61,negated_conjecture,
    ( ne(esk1_0)
    & ap(c_2Einteger__word_2Ei2w(esk1_0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) != ap(c_2Ewords_2En2w(esk1_0),c_2Enum_2E0) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).

cnf(c_0_62,plain,
    ( ap(c_2Einteger__word_2Ei2w(X1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = ap(c_2Ewords_2En2w(X1),c_2Enum_2E0)
    | ~ mem(ap(c_2Ewords_2En2w(X1),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,X1))
    | ~ ne(ty_2Efcp_2Ecart(bool,X1))
    | ~ ne(X1) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_63,plain,
    ( mem(ap(c_2Ewords_2En2w(X1),X2),ty_2Efcp_2Ecart(bool,X1))
    | ~ mem(X2,ty_2Enum_2Enum)
    | ~ ne(X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_60]) ).

cnf(c_0_64,negated_conjecture,
    ap(c_2Einteger__word_2Ei2w(esk1_0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) != ap(c_2Ewords_2En2w(esk1_0),c_2Enum_2E0),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_65,plain,
    ( ap(c_2Einteger__word_2Ei2w(X1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = ap(c_2Ewords_2En2w(X1),c_2Enum_2E0)
    | ~ ne(ty_2Efcp_2Ecart(bool,X1))
    | ~ ne(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_38])]) ).

cnf(c_0_66,negated_conjecture,
    ne(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

fof(c_0_67,plain,
    ! [X62,X63] :
      ( ~ ne(X62)
      | ~ ne(X63)
      | ne(ty_2Efcp_2Ecart(X62,X63)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ne_ty_2Efcp_2Ecart])])])]) ).

cnf(c_0_68,negated_conjecture,
    ~ ne(ty_2Efcp_2Ecart(bool,esk1_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66])]) ).

cnf(c_0_69,plain,
    ( ne(ty_2Efcp_2Ecart(X1,X2))
    | ~ ne(X1)
    | ~ ne(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_70,plain,
    ne(bool),
    inference(split_conjunct,[status(thm)],[bool_ne]) ).

cnf(c_0_71,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_66]),c_0_70])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : ITP015+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.06/0.11  % Command    : run_E %s %d THM
% 0.10/0.31  % Computer : n027.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri May  3 13:07:21 EDT 2024
% 0.16/0.32  % CPUTime    : 
% 0.16/0.43  Running first-order model finding
% 0.16/0.43  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.HkXXY463pE/E---3.1_9643.p
% 3.54/0.88  # Version: 3.1.0
% 3.54/0.88  # Preprocessing class: FSLSSMSMSSSNFFN.
% 3.54/0.88  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.54/0.88  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.54/0.88  # Starting new_bool_3 with 300s (1) cores
% 3.54/0.88  # Starting new_bool_1 with 300s (1) cores
% 3.54/0.88  # Starting sh5l with 300s (1) cores
% 3.54/0.88  # sh5l with pid 9723 completed with status 0
% 3.54/0.88  # Result found by sh5l
% 3.54/0.88  # Preprocessing class: FSLSSMSMSSSNFFN.
% 3.54/0.88  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.54/0.88  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.54/0.88  # Starting new_bool_3 with 300s (1) cores
% 3.54/0.88  # Starting new_bool_1 with 300s (1) cores
% 3.54/0.88  # Starting sh5l with 300s (1) cores
% 3.54/0.88  # SinE strategy is gf500_gu_R04_F100_L20000
% 3.54/0.88  # Search class: FGHSF-FFMM31-DFFFFFNN
% 3.54/0.88  # partial match(1): FGHSF-FFMM31-SFFFFFNN
% 3.54/0.88  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 3.54/0.88  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 163s (1) cores
% 3.54/0.88  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with pid 9726 completed with status 0
% 3.54/0.88  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN
% 3.54/0.88  # Preprocessing class: FSLSSMSMSSSNFFN.
% 3.54/0.88  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.54/0.88  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.54/0.88  # Starting new_bool_3 with 300s (1) cores
% 3.54/0.88  # Starting new_bool_1 with 300s (1) cores
% 3.54/0.88  # Starting sh5l with 300s (1) cores
% 3.54/0.88  # SinE strategy is gf500_gu_R04_F100_L20000
% 3.54/0.88  # Search class: FGHSF-FFMM31-DFFFFFNN
% 3.54/0.88  # partial match(1): FGHSF-FFMM31-SFFFFFNN
% 3.54/0.88  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 3.54/0.88  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 163s (1) cores
% 3.54/0.88  # Preprocessing time       : 0.002 s
% 3.54/0.88  # Presaturation interreduction done
% 3.54/0.88  
% 3.54/0.88  # Proof found!
% 3.54/0.88  # SZS status Theorem
% 3.54/0.88  # SZS output start CNFRefutation
% See solution above
% 3.54/0.88  # Parsed axioms                        : 57
% 3.54/0.88  # Removed by relevancy pruning/SinE    : 16
% 3.54/0.88  # Initial clauses                      : 75
% 3.54/0.88  # Removed in clause preprocessing      : 24
% 3.54/0.88  # Initial clauses in saturation        : 51
% 3.54/0.88  # Processed clauses                    : 3550
% 3.54/0.88  # ...of these trivial                  : 3
% 3.54/0.88  # ...subsumed                          : 2200
% 3.54/0.88  # ...remaining for further processing  : 1347
% 3.54/0.88  # Other redundant clauses eliminated   : 66
% 3.54/0.88  # Clauses deleted for lack of memory   : 0
% 3.54/0.88  # Backward-subsumed                    : 425
% 3.54/0.88  # Backward-rewritten                   : 18
% 3.54/0.88  # Generated clauses                    : 14240
% 3.54/0.88  # ...of the previous two non-redundant : 11713
% 3.54/0.88  # ...aggressively subsumed             : 0
% 3.54/0.88  # Contextual simplify-reflections      : 34
% 3.54/0.88  # Paramodulations                      : 14111
% 3.54/0.88  # Factorizations                       : 50
% 3.54/0.88  # NegExts                              : 0
% 3.54/0.88  # Equation resolutions                 : 79
% 3.54/0.88  # Disequality decompositions           : 0
% 3.54/0.88  # Total rewrite steps                  : 12120
% 3.54/0.88  # ...of those cached                   : 12090
% 3.54/0.88  # Propositional unsat checks           : 0
% 3.54/0.88  #    Propositional check models        : 0
% 3.54/0.88  #    Propositional check unsatisfiable : 0
% 3.54/0.88  #    Propositional clauses             : 0
% 3.54/0.88  #    Propositional clauses after purity: 0
% 3.54/0.88  #    Propositional unsat core size     : 0
% 3.54/0.88  #    Propositional preprocessing time  : 0.000
% 3.54/0.88  #    Propositional encoding time       : 0.000
% 3.54/0.88  #    Propositional solver time         : 0.000
% 3.54/0.88  #    Success case prop preproc time    : 0.000
% 3.54/0.88  #    Success case prop encoding time   : 0.000
% 3.54/0.88  #    Success case prop solver time     : 0.000
% 3.54/0.88  # Current number of processed clauses  : 845
% 3.54/0.88  #    Positive orientable unit clauses  : 31
% 3.54/0.88  #    Positive unorientable unit clauses: 0
% 3.54/0.88  #    Negative unit clauses             : 4
% 3.54/0.88  #    Non-unit-clauses                  : 810
% 3.54/0.88  # Current number of unprocessed clauses: 7688
% 3.54/0.88  # ...number of literals in the above   : 40466
% 3.54/0.88  # Current number of archived formulas  : 0
% 3.54/0.88  # Current number of archived clauses   : 497
% 3.54/0.88  # Clause-clause subsumption calls (NU) : 73566
% 3.54/0.88  # Rec. Clause-clause subsumption calls : 22701
% 3.54/0.88  # Non-unit clause-clause subsumptions  : 1819
% 3.54/0.88  # Unit Clause-clause subsumption calls : 704
% 3.54/0.88  # Rewrite failures with RHS unbound    : 0
% 3.54/0.88  # BW rewrite match attempts            : 71
% 3.54/0.88  # BW rewrite match successes           : 18
% 3.54/0.88  # Condensation attempts                : 0
% 3.54/0.88  # Condensation successes               : 0
% 3.54/0.88  # Termbank termtop insertions          : 553412
% 3.54/0.88  # Search garbage collected termcells   : 1372
% 3.54/0.88  
% 3.54/0.88  # -------------------------------------------------
% 3.54/0.88  # User time                : 0.424 s
% 3.54/0.88  # System time              : 0.014 s
% 3.54/0.88  # Total time               : 0.437 s
% 3.54/0.88  # Maximum resident set size: 2004 pages
% 3.54/0.88  
% 3.54/0.88  # -------------------------------------------------
% 3.54/0.88  # User time                : 0.425 s
% 3.54/0.88  # System time              : 0.016 s
% 3.54/0.88  # Total time               : 0.441 s
% 3.54/0.88  # Maximum resident set size: 1792 pages
% 3.54/0.88  % E---3.1 exiting
%------------------------------------------------------------------------------